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Pebble Hunting: The Value of Billy Hamilton

One week ago, in a game against the Angels, Chone Figgins pinch-ran. Ten years ago, in a game with the Angels, Chone Figgins also pinch-ran, in his major-league debut, scoring the winning run on a squeeze bunt. Things are always coming full circle, except I guess for Chone Figgins in the most literal sense, because even if he comes around to score after pinch-running he will have completed only 270 degrees.

Wait, come back! This is not a piece about Chone Figgins or geometry. It’s about Billy Hamilton, I promise. Here, watch a video of Billy Hamilton:

The Angels brought Figgins up in August 2002, used him almost exclusively as a pinch-runner, then put him on the postseason roster, where he was used exclusively as a pinch-runner. It led to good things, such as the tying run in the Angels’ Game 6 comeback against the Giants. As Mike Scioscia reminisced years later,

"G.A. hits the blooper down the line, Figgy pushes the action and forces a misplay by Bonds, and we end up with second and third," Scioscia said. "That's the way Chone played. Hopefully, Jeremy will play with that same fearlessness."

Jeremy was Jeremy Moore, another fleet pair of feet who spent a September pinch-running for the Angels. In a world with 12- and 13-man bullpens, it’s hard to carry a player who does nothing but run, but that rule doesn’t apply to September. Depending on the philosophy of the manager, it might also not apply to October.

So here we have Billy Hamilton, running around the minor leagues like he’s on Gummiberry Juice, and here we have the Reds, playing meaningful games in September and (probably) October. If Manny Machado’s bat can help in September, and Dylan Bundy's arm could help in September, then surely Hamilton’s legs could help in September. What follows is an attempt to figure out how much baseball’s greatest runner could be worth if he were highly leveraged for a month.

The Reds play 29 games after August this year. I took the Reds' final 29 games of the 2011 season and plopped a Billy Hamilton pinch-running appearance wherever a Billy Hamilton pinch-running appearance would have helped. I used the Reds' final 29 games of 2011 for no significant reason. I could have used any 29 games; just trying to find typical baseball games. And, of course, the butterfly effect makes any extrapolation even within our sample games suspect. Except have you ever tried to catch a butterfly? Them suckers are quick. Like Billy Hamilton!

So, the rules: Hamilton can run only in the sixth inning or later. Once he runs, I’m taking him out of the game. I’m not giving him any credit for baseball skills other than legs, so it's just running and then gone. I didn’t know the outcome of the game when I was deciding when to use him. That led to instances where I used Hamilton, then wished I had him later. Tough luck, 2011 Reds. Dems the breaks.

I’m going to send him virtually every single time he is on first base. The reason I’m going to do this is because Billy Hamilton runs every single time he gets to first base, basically. In his first 20 games at Double-A Pensacola, he reached first base (with an open second base) 20 times. He was balked to second once and attempted to steal 16 of the other 19 times. I presume he was thwarted by teammates swinging early in the count the other three times.

I’m not going to send him when he gets to second, unless the win expectancy of the situation really, really favors it. He attempted to steal third base just three times out of 15 opportunities in those first 20 games at Pensacola. (He did move to third base on throwing errors twice. Defenses go nuts when Billy Hamilton appears.)

I will have him be thrown out in 18 percent of his attempted steals. I had a hard time deciding on this number; he is at 82.7 percent success in his career, but that success rate has declined each time he has moved up a level. Nate Silver wrote in 2006 that "CS is one of those stats that doesn't 'translate' meaningfully to the major-league level," and to simplify I’m going with 82 percent. Obviously, this is adjustable, and you might wish I adjusted it.

I used the win expectancy table from The Book.

That was a lot of rules. You are bored. Watch this:

So, 29 games. Of the 29, 14 offered no situation in which Billy Hamilton’s legs would have been useful. A properly leveraged Billy Hamilton would run in about half of his team’s games.

Game

Inning

Score

Baserunners

Outs

Replacing

8/29/2011

B6

Tie

1

0

Hanigan

8/30/2011

–

–

–

–

–

8/31/2011

B9

-3

1(23)

2

Cairo

9/1/2011

B7

-2

1

1

Renteria

9/2/2011

T9

1

1(2)

1

Cairo

9/3/2011

–

–

–

–

–

9/4/2011

T10

Tie

1

2

Alonso

9/5/2011

–

–

–

–

9/6/2011

T9

2

1

2

Frazier

9/7/2011

T7

-2

1(3)

2

Renteria

9/9/2011

T9

3

1

1

Alonso

9/10/2011

–

–

–

–

–

9/11/2011

–

–

–

–

–

9/12/2011

–

–

–

–

–

9/13/2011

–

–

–

–

–

9/14/2011

–

–

–

–

–

9/15/2011

B7

2

1

0

Alonso

9/16/2011

–

–

–

–

–

9/17/2011

–

–

–

–

–

9/18/2011

–

–

–

–

–

9/19/2011

B7

Tie

1

2

Hernandez

9/20/2011

–

–

–

–

–

9/21/2011

B6

2

1

1

Heisey

9/23/2011

T8

-1

1

2

Hernandez

9/24/2011

T8

-1

1

2

Renteria

9/25/2011

T8

2

1

2

Alonso

9/26/2011

–

–

–

–

–

9/27/2011

T-9

-1

1

1

Mesoraco

9/28/2011

–

–

–

–

–

In two of those games, there would have been no way for him to steal, because of the runners on ahead of him. In one, a stolen base made no strategic sense. So there are 12 stolen base attempts. Taking the win expectancy of the situation, the win probability added of a stolen base, the win probability decrease of a caught stealing, and an expected 82 percent success rate, we get this table and the words summing it up underneath.

So all that running adds up to 0.11 wins. Awwwwww. That’s so boring. What a boring conclusion! Can it be so? After all, Dave Roberts!

But Dave Roberts’ stolen base in the 2004 ALCS is instructive. The Red Sox’ chances of winning the game with him on first were about 35 percent. With him on second, they jumped up to 46 percent. That’s huge. But if he’d been caught stealing, their chances would have dropped to 12 percent. That’s huge. Even assuming an 82 percent success rate, the net gain of a stolen base attempt in that situation is less than 1/20th of a win. And leveraged opportunities like that are rare.

There are so many other factors. Is 82 percent a fair rate? How often does Hamilton steal successfully when the other team knows he’s running? What about when he knows he can’t get caught? If he were 100 percent successful, he'd add about a quarter of a win. If he were 75 percent successful, his value would drop to almost zero.

And stolen bases are just a small part of this. Hamilton might score from first on a double that would send somebody else only to third. (Though in his minor-league career, that has almost never happened, because Hamilton never stays at first.) He might cause the pitcher to balk, or his stolen base attempt might cause the catcher to throw a ball into center field. (His appearance might also cost the Reds their starting left fielder or third baseman or catcher for the rest of the game.) He might take away the pitcher’s focus and give his teammate at the plate a better chance. (He might also cause his teammate to take a strike so that Hamilton can steal). There are wild pitches, passed balls, sacrifice flies, fielder’s choices, errant pick-off throws, and there’s pushing the action and forcing Barry Bonds to misplay it.

No, a pinch-running Billy Hamilton isn’t likely to win multiple games for the Reds in the span of a month, no matter how smartly he is deployed. But, finally, there’s this: 0.11 wins sure isn’t nothing, if it’s the right 0.11 win.

Assuming that those 29 games are in fact a random sample of all baseball games, you could use this to figure out how much he helps in the playoffs as well.
(.11)/29 = .00379, or around 4 thousandths of a win per game. It seems like someone could turn that into expected increased win expectancy for having Billy Hamilton on the playoff roster.
The question for the Reds, then, is whether that small increase in win expectancy is worth dumping their 12th or 13th pitcher. My guess is yes. But the difference is probably small enough that intangibles could make a difference. Maybe that 13th pitcher is a great presence in the clubhouse, or is buddies with Joey Votto, or whatever other reason you'd want to keep him around.

Fun article, Sam. But I absolutely love that line in the 3rd-last graf - "How often does Hamilton steal successfully when the other team knows he's running?".
What's his SB% again? Because at this point, the other team should always know that he's running.

You assume A ball catchers and pitchers, sometimes kids just out of college or high school, will perform the same as major league catchers and pitchers. His SB% now most likely won't be his SB% in the major leagues.

First of all, hilarious stuff as usual.
Secondly, I wonder if the 6th-inning-or-later limitation you imposed may be too restrictive, particularly given the expanded roster (allowing for a better bat to be subbed in for Hamilton after deploying him in an early inning where a highly leveraged Dave Roberts-like situation presents itself), and the fact that in your model, Slidin' Billy wasn't used at all in half the games.

I'm sure it looks much different in person, but Hamilton simply doesn't LOOK fast to me when he's running. I don't know how to describe it other than it's just like other people are doing things more slowly than normal. It's that same kind of feel when you watch Usain Bolt run. It's not that his legs are churning faster than everybody else, he seems to move further with each strike...

Yes, as noted by one of the announcers during the Olympics, Bolt's stride is 10 feet at full speed, and that he only take 40-41 strides during the 100 (compared to 45-47 more typically). It may be that BH is taking fewer strides between bases, which would seem to be an important stat in basestealing.

It's like the opposite of watching Bryce Harper run. Harper has so many flailing pieces, he looks faster because a lot is happening and he's hustling. Then watch Mike Trout run, it's smooth. Hamilton isn't as smooth, but he's quieter than other speed guys. I think Stubbs is a quiet runner with plus speed as well.

You almost lost me when you said that, contrary to your lede, this was NOT a piece about geometry. This is Baseball Prospectus - I expect to find myself swimming in all sorts of math when I read the site. The prospect of you somehow adding geometry (perhaps Euclidean, or, dare I dream, non-Euclidean) to the usual math found here greatly excited me. Then, to be denied geometry - not cool.
Fortunately, your generous offer of a Billy Hamilton video kept me reading. But the next time you offer geometry, Sam, I expect you to deliver. If Matt can work modus ponens into a Daily Hit List, certainly you can find a place for geometry in one of your articles.
;)

Watching the first video, it looks like Hamilton is really bad at sliding feet-first, almost as if he has to slow himself down while in a standing position before he hits the ground.
Maybe that's what you have to do to slide feet-first when you're that fast though. I would have no earthly idea.